Abstract
Given a matrix over the ring of differential polynomials, we show how to compute the Hermite form H of A and a unimodular matrix U such that UA = H. The algorithm requires a polynomial number of operations in F in terms of n, , . When F = ℚ it require time polynomial in the bit-length of the rational coefficients as well.
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Giesbrecht, M., Kim, M.S. (2009). On Computing the Hermite Form of a Matrix of Differential Polynomials. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2009. Lecture Notes in Computer Science, vol 5743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04103-7_12
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DOI: https://doi.org/10.1007/978-3-642-04103-7_12
Publisher Name: Springer, Berlin, Heidelberg
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